STRONG CONVERGENCE ANALYSIS OF A HYBRID ALGORITHM FOR NONLINEAR OPERATORS IN A BANACH SPACE

DOI10.11948/2018.19OpenAlexW2784026446MaRDI QIDQ5147797

Sun Young Cho

Publication date: 28 January 2021

Published in: Journal of Applied Analysis & Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.11948/2018.19

zbMATH Keywords

variational inequalityequilibrium problemgeneralized projectionquasi-\( \phi \)-nonexpansive mapping

Mathematics Subject Classification ID

Variational and other types of inequalities involving nonlinear operators (general) (47J20) Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming) (90C33)

Related Items

A conjugate gradient algorithm for large-scale unconstrained optimization problems and nonlinear equations ⋮ Well-posedness for a class of generalized variational-hemivariational inequalities involving set-valued operators ⋮ Geometric inequalities for solving variational inequality problems in certain Banach spaces ⋮ Strong convergence theorems for solving pseudo-monotone variational inequality problems and applications ⋮ Tseng's extragradient algorithm for pseudomonotone variational inequalities on Hadamard manifolds ⋮ Strong convergence of an extragradient-like algorithm involving pseudo-monotone mappings ⋮ Multivariate systems of nonexpansive operator equations and iterative algorithms for solving them in uniformly convex and uniformly smooth Banach spaces with applications ⋮ A Novel Halpern-type Algorithm for a Monotone Inclusion Problem and a Fixed Points Problem on Hadamard Manifolds ⋮ A subgradient extragradient algorithm with inertial effects for solving strongly pseudomonotone variational inequalities ⋮ Unnamed Item ⋮ A fixed point method for solving a split feasibility problem in Hilbert spaces ⋮ Robust optimization model for uncertain multiobjective linear programs ⋮ The split feasibility problems in an infinite dimensional space ⋮ An iterative method and weak sharp solutions for multitime-type variational inequalities ⋮ Parallel proximal point methods for systems of vector optimization problems on Hadamard manifolds without convexity ⋮ Modified inertial subgradient extragradient algorithms for pseudomonotone equilibrium problems with the constraint of nonexpansive mappings ⋮ Continuous-time ergodic algorithm for solving monotone variational inequalities ⋮ Iterative methods for fixed point problems and generalized split feasibility problems in Banach spaces ⋮ Higher-order weak radial epiderivatives and non-convex set-valued optimization problems ⋮ On iterative solutions of a split feasibility problem with nonexpansive mappings ⋮ Composite inertial subgradient extragradient methods for variational inequalities and fixed point problems ⋮ Composite extragradient implicit rule for solving a hierarchical variational inequality with constraints of variational inclusion and fixed point problems ⋮ Iterative methods for fixed points and zero points of nonlinear mappings with applications ⋮ A new hybrid projection algorithm for equilibrium problems and asymptotically quasi \(\phi \)-nonexpansive mappings in Banach spaces ⋮ Weak and strong convergence of inertial Tseng's extragradient algorithms for solving variational inequality problems ⋮ Two inertial subgradient extragradient algorithms for variational inequalities with fixed-point constraints ⋮ Unnamed Item ⋮ ON THE STRONG CONVERGENCE OF A PROJECTION-BASED ALGORITHM IN HILBERT SPACES ⋮ AN INERTIAL SHRINKING PROJECTION ALGORITHM FOR SPLIT COMMON FIXED POINT PROBLEMS ⋮ ACCELERATED PROJECTION-BASED FORWARD-BACKWARD SPLITTING ALGORITHMS FOR MONOTONE INCLUSION PROBLEMS ⋮ Difference gap functions and global error bounds for random mixed equilibrium problems ⋮ Variational inequalities, variational inclusions and common fixed point problems in Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convergence analysis of an iterative algorithm for monotone operators
• Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces
• On asymptotically quasi-\(\phi\)-nonexpansive mappings in the intermediate sense
• Hybrid algorithms of nonexpansive semigroups for mixed equilibrium problems, variational inequalities, and fixed point problems
• A regularization projection algorithm for various problems with nonlinear mappings in Hilbert spaces
• On hybrid projection methods for asymptotically quasi-\(\phi\)-nonexpansive mappings
• Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces
• Characterization of the subdifferentials of convex functions
• Generalized mixed equilibrium and fixed point problems in a Banach space
• A monotone projection algorithm for solving fixed points of nonlinear mappings and equilibrium problems
• Convergence of iterates of asymptotically nonexpansive mappings in Banach spaces with the uniform Opial property
• Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
• Metric and Generalized Projection Operators in Banach Spaces: Properties and Applications
• WEAK CONVERGENCE OF A SPLITTING ALGORITHM IN HILBERT SPACES
• On fixed point and variational inclusion problems
• Generalized Projection Algorithms for Nonlinear Operators